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Archimedes, a scientist from the Ancient Greece, discovered 13 types of polyhedra, called now as Archimedean solids, which are also referred as semi-regular polyhedra.
Each of them is limited by different types of regular polygons where the polyhedral angles and identical polygons are equal. Furthermore, the same number of equal faces meets at each vertex. In the same order each of these solids can be inscribed into a sphere.
In natural environments regular polyhedra can be found in the form of crystals (minerals).
Sodium sulphate reminds the shape of tetrahedron.
Quite often a question about a practical use of paper models pops up. What is the point of paper modeling?
One can specify the following mathematical characteristics in each of the five Platonic solids:
1. The radius of the sphere circumscribing the polyhedron;
2. The radius of the sphere inscribed in the polyhedron;
3. The surface area of the polyhedron;
4. The volume of the polyhedron.
Architects have used the elements of polyhedra in designing their constructions since ancient times. Nowadays this approach distinguishes buildings among thousands of others.
The Ministry of Defense in USA has the shape of a regular pentagon.
A polyhedron is a solid bounded by flat polygons, which are called faces. Sides of the faces are called edges, and their corners are called as vertices. Depending on the number of faces one can specify tetrahedron (4 faces), pentahedron (5 faces), etc. A polyhedron is considered to be convex if it is located on one side of the plane of each of its faces. A polyhedron is called regular if its faces are regular polygons (i.e., where all sides and angles are equal) and all polyhedral angles at the vertices are equal. There can be found five types of regular polyhedra: tetrahedron, cube (regular hexahedron), octahedron, dodecahedron, icosahedron.
Is it possible to make up an icosahedron using more simple polyhedra?
In geometry the section which deals with three-dimensional figures is called stereometry. The word “stereometry” comes from Ancient Greece and is derived from the word “stereos”, which means “solid”, and the word “metreo”, which means “to measure”.
Young British designer, Richard Sweeney, creates amazing paper sculptures. It is interesting that regular polyhedra are the basis for many of them. On his website http://www.richardsweeney.co.uk he even gives the names of regular polyhedra to the created geometric shapes.